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  • 1.
    Axehill, Daniel
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Lindqvist, Kristian
    Scania.
    Adaptive Cruise Control for Heavy Vehicles2004Inngår i: Proceedings of Reglermöte 2004, 2004Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    An Adaptive Cruise Controller (ACC) is an extension of an ordinary cruise controller. In addition to maintaining a desired set speed, an ACC can also maintain a desired time gap to the vehicle ahead. For this end, both the engine and the brakes are controlled. The interest in the MPC-controller as a solution to the problem was to achieve automatic actuator switching, thus with no explicitly defined switch points. The MPC-controller is based on a model of the system including bounds on the control signals and on linear combinations of the states. Using this knowledge, the MPC-controller will choose the correct actuator for the current driving situation. Among the drawbacks, it can be mentioned that the variant of MPC, used in this paper, is too complex to implement in the control system currently used in trucks.

  • 2.
    Gerdin, Markus
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för systemteknik, Reglerteknik.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Nonlinear Stochastic Differential-Algebraic Equations with Application to Particle Filtering2006Inngår i: Proceedings of the 45th IEEE Conference on Decision and Control, 2006, s. 6630-6635Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Differential-algebraic equation (DAE) models naturally arise when modeling physical systems from first principles. To be able to use such models for state estimation procedures such as particle filtering, it is desirable to include a noise model. This paper discusses well-posedness of differential-algebraic equations with noise models, here denoted stochastic differential-algebraic equations. Since the exact conditions are rather involved, approximate implementation methods are also discussed. It is also discussed how a particle filter can be implemented for DAE models, and how the approximate implementation methods can be used for particle filtering. Finally, the particle filtering methods are exemplified by implementation of a particle filter for a DAE model.

  • 3.
    Gerdin, Markus
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Nonlinear Stochastic Differential-Algebraic Equations with Application to Particle Filtering2007Rapport (Annet vitenskapelig)
    Abstract [en]

    Differential-algebraic equation (DAE) models naturally arise when modeling physical systems from first principles. To be able to use such models for state estimation procedures such as particle filtering, it is desirable to include a noise model. This paper discusses well-posedness of differential-algebraic equations with noise models, here denoted stochastic differential-algebraic equations. Since the exact conditions are rather involved, approximate implementation methods are also discussed. It is also discussed how a particle filter can be implemented for DAE models, and how the approximate implementation methods can be used for particle filtering. Finally, the particle filtering methods are exemplified by implementation of a particle filter for a DAE model.

  • 4.
    Glad, Torkel
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hamilton-Jacobi Equations for Nonlinear Descriptor Systems2006Inngår i: Proceedings of the 2006 American Control Conference, 2006, s. 1027-1031Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Optimal control problems for nonlinear descriptor systems are considered. Anapproach where the descriptor system is conceptually reduced to a state spaceform is compared to an approach where the Hamilton-Jacobi equation is directly formulated for the descriptor system. The two approaches are shown to give essentially the same systems of equations to be solved. A certain unknown function is present only in the second approach but is shown to be computable from the quantities common to both approches.

  • 5.
    Glad, Torkel
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hamilton-Jacobi Equations for Nonlinear Descriptor Systems2005Rapport (Annet vitenskapelig)
    Abstract [en]

    Optimal control problems for nonlinear descriptor systems are considered. Anapproach where the descriptor system is conceptually reduced to a state spaceform is compared to an approach where the Hamilton-Jacobi equation is directly formulated for the descriptor system. The two approaches are shown to give essentially the same systems of equations to be solved. A certain unknown function is present only in the second approach but is shown to be computable from the quantities common to both approches.

  • 6.
    Isaksson, Alf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten. Corp Research, Sweden.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik. Volvo Construct Equipment, Sweden.
    Tornqvist, David
    SenionLab AB, S-58330 Linkoping, Sweden.
    Ljung, Lennart
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Kok, Manon
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Using horizon estimation and nonlinear optimization for grey-box identification2015Inngår i: Journal of Process Control, ISSN 0959-1524, E-ISSN 1873-2771, Vol. 30, s. 69-79Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An established method for grey-box identification is to use maximum-likelihood estimation for the nonlinear case implemented via extended Kalman filtering. In applications of (nonlinear) model predictive control a more and more common approach for the state estimation is to use moving horizon estimation, which employs (nonlinear) optimization directly on a model for a whole batch of data. This paper shows that, in the linear case, horizon estimation may also be used for joint parameter estimation and state estimation, as long as a bias correction based on the Kalman filter is included. For the nonlinear case two special cases are presented where the bias correction can be determined without approximation. A procedure how to approximate the bias correction for general nonlinear systems is also outlined. (C) 2015 Elsevier Ltd. All rights reserved.

  • 7.
    Isaksson, Alf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan. ABB AB, Sweden.
    Törnqvist, David
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ljung, Lennart
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Grey-Box Identification Based on Horizon Estimation and Nonlinear Optimization2009Inngår i: Proceedings of the 41st ISCIE International Symposium on Stochastic Systems, Institute of Systems, Control and Information Engineers , 2009, s. 1-6Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In applications of (nonlinear) model predictive control a more and more common approach for the state estimation is to use moving horizon estimation, which employs (nonlinear) optimization directly on a model for a whole batch of data. This paper shows that horizon estimation may also be used for joint parameter estimation and state estimation, as long as a bias correction based on the Kalman filter is included. A procedure how to approximate the bias correction for nonlinear systems is outlined.

  • 8.
    Isaksson, Alf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Törnqvist, David
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ljung, Lennart
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Grey-Box Identification Based on Horizon Estimation and Nonlinear Optimization2010Rapport (Annet vitenskapelig)
    Abstract [en]

    In applications of (nonlinear) model predictive control a more and more common approach for the state estimation is to use moving horizon estimation, which employs (nonlinear) optimization directly on a model for a whole batch of data. This paper shows that horizon estimation may also be used for joint parameter estimation and state estimation, as long as a bias correction based on the Kalman filter is included. A procedure how to approximate the bias correction for nonlinear systems is outlined.

  • 9.
    Karlsson, Rickard
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Törnqvist, David
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hol, Jeroen
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hansson, Anders
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Positioning and Control of an Unmanned Aerial Vehicle2006Inngår i: Proceedings of the 2nd International CDIO Conference and Collaborators' Meeting, 2006Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In the CDIO-project course in Automatic Control, an Autonomous Unmanned Aerial vehicle (UAV) is constructed, utilizing an existing radio controlled model aircraft. By adding an inertial sensor measuring acceleration and rotation, together with a Global Positioning System (GPS) sensor, the aim is to construct an accurate positioning system. This is used by an on board computer to calculate rudder control signals to a set of DC-servos in order to follow a predefined way-point trajectory. The project involves 17 students, which is roughly three times as big as previous projects, and it comprises both positioning, control, and hardware design. Since the project is still ongoing some preliminary results and conclusions are presented.

  • 10.
    Karlsson, Rickard
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Törnqvist, David
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hol, Jeroen
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hansson, Anders
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Positioning and Control of an Unmanned Aerial Vehicle2006Rapport (Annet vitenskapelig)
    Abstract [en]

    In the CDIO-project course in Automatic Control, an Autonomous Unmanned Aerial vehicle (UAV) is constructed, utilizing an existing radio controlled model aircraft. By adding an inertial sensor measuring acceleration and rotation, together with a Global Positioning System (GPS) sensor, the aim is to construct an accurate positioning system. This is used by an on board computer to calculate rudder control signals to a set of DC-servos in order to follow a predefined way-point trajectory. The project involves 17 students, which is roughly three times as big as previous projects, and it comprises both positioning, control, and hardware design. Since the project is still ongoing some preliminary results and conclusions are presented.

  • 11.
    Linder, Jonas
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Enqvist, Martin
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Identifiability of physical parameters in systems with limited sensors2014Inngår i: Proceedings of the 19th IFAC World Congress, 2014, s. 6454-6459Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper, a method for estimating physical parameters using limited sensors is investigated. As a case study, measurements from an IMU are used for estimating the change in mass and the change in center of mass of a ship. The roll motion is studied and an instrumental variable method estimating the parameters of a transfer function from the tangential acceleration to the angular velocity is presented. It is shown that only a subset of the unknown parameters are identifiable simultaneously. A multi-stage identification approach is presented as a remedy for this. A limited simulation study is also presented to show the properties of the estimator. This shows that the method is indeed promising but that more work is needed to reduce the variance of the estimator.

  • 12.
    Linder, Jonas
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Lindkvist, Simon
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Two-Step Framework for Interactive Multi-Objective Optimization2012Rapport (Annet vitenskapelig)
    Abstract [en]

    In many real-world optimization applications there are often a number of conflicting objective functions that are all important to optimize. The purpose of multiobjective optimization (MOO) is to give the decision maker(DM) an understanding of how these functions are conflicting and the possibility to choose an appropriate trade-off between them. There are multiple methods for solving MOO problems but the focus in this paper is on interactive methods. When the size and complexity of the MOO problem grows the time needed to find a solution is too long to yield a pleasant experience for the DM. In this paper, a method to replace the original MOO problem with an approximation is suggested to speed up the process. The approximation is created and used in a two-step framework which makes it possible to investigate the Pareto frontier in real-time and that can handle nonlinear and non-convex MOO problems with m objective functions. The first step generates a number of samples of the complete Pareto frontier which is sparse but dense enough for the approximation. The second stepis an interactive tool for the DM to use to continuously and in real-time navigate on the approximated Pareto set in both objective- and decision space. The tool is used to investigate the Pareto frontier and to find a preferred solution. A method of decomposing the approximated set into simplices has been developed using Delaunay triangulation. This methodis able to make a good approximation for sets that are non-convex. The method is also able to handle disconnected sets and holes. This makes it possible to change the feasible region in both decision- and objective space. The framework is demonstrated on three example problems that show the functionality and performance of the implemented framework.

  • 13.
    Liu, Bin
    et al.
    ABB Corp Research Centre, Sweden.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik. Linköpings universitet, Tekniska fakulteten.
    Laiho, Antti
    ABB, Finland.
    Optimization-based radial active magnetic bearing controller design and verification for flexible rotors2016Inngår i: Proceedings of the Institution of mechanical engineers. Part I, journal of systems and control engineering, ISSN 0959-6518, E-ISSN 2041-3041, Vol. 230, nr 4, s. 339-351Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Engineering costs, especially cost for controller design, are substantial and obstruct active magnetic bearings for broader industrial applications. An optimization-based active magnetic bearing controller design method is developed to solve this problem. Optimization criteria are selected to describe active magnetic bearing practical performance. Controller components are chosen considering that the parameters can be manually interpreted and modified on-site for commissioning. A multi-objective optimization toolbox can be used to tune the controller parameters automatically by minimizing the optimization criteria. The method has been verified within a controller design process for an active magnetic bearing levitated machine. With this method, engineering effort for controller design can be reduced significantly.

  • 14.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Computation of Upper Bound on the L2-gain for Polynomial Differential-Algebraic Systems, using Sum of Squares Decomposition2007Rapport (Annet vitenskapelig)
  • 15.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Descriptor Systems and Control Theory2005Rapport (Annet vitenskapelig)
    Abstract [en]

    This report is a brief survey over different concepts and methods concerning singular systems. Singular system is also called differential algebraic equations (DAE) since a DAE model may involve both differential and algebraic equations. There is an growing interest in DAE systems much depending on the increased usage of object oriented modeling languages, like Modelica, in the modeling of dynamical systems. These programs often give DAE models as result. Another advantage of DAE models is that they sometimes can keep the natural structure of the dynamical model.

  • 16.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Optimal Control and Model Reduction of Nonlinear DAE Models2008Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    In this thesis, different topics for models that consist of both differential and algebraic equations are studied. The interest in such models, denoted DAE models, have increased substantially during the last years. One of the major reasons is that several modern object-oriented modeling tools used to model large physical systems yield models in this form. The DAE models will, at least locally, be assumed to be described by a decoupled set of ordinary differential equations and purely algebraic equations. In theory, this assumption is not very restrictive because index reduction techniques can be used to rewrite rather general DAE models to satisfy this assumption.

    One of the topics considered in this thesis is optimal feedback control. For state-space models, it is well-known that the Hamilton-Jacobi-Bellman equation (HJB) can be used to calculate the optimal solution. For DAE models, a similar result exists where a Hamilton-Jacobi-Bellman-like equation is solved. This equation has an extra term in order to incorporate the algebraic equations, and it is investigated how the extra term must be chosen in order to obtain the same solution from the different equations.

    A problem when using the HJB to find the optimal feedback law is that it involves solving a nonlinear partial differential equation. Often, this equation cannot be solved explicitly. An easier problem is to compute a locally optimal feedback law. For analytic nonlinear time-invariant state-space models, this problem was solved in the 1960's, and in the 1970's the time-varying case was solved as well. In both cases, the optimal solution is described by convergent power series. In this thesis, both of these results are extended to analytic DAE models.

    Usually, the power series solution of the optimal feedback control problem consists of an infinite number of terms. In practice, an approximation with a finite number of terms is used. A problem is that for certain problems, the region in which the approximate solution is accurate may be small. Therefore, another parametrization of the optimal solution, namely rational functions, is studied. It is shown that for some problems, this parametrization gives a substantially better result than the power series approximation in terms of approximating the optimal cost over a larger region.

    A problem with the power series method is that the computational complexity grows rapidly both in the number of states and in the order of approximation. However, for DAE models where the underlying state-space model is control-affine, the computations can be simplified. Therefore, conditions under which this property holds are derived.

    Another major topic considered is how to include stochastic processes in nonlinear DAE models. Stochastic processes are used to model uncertainties and noise in physical processes, and are often an important part in for example state estimation. Therefore, conditions are presented under which noise can be introduced in a DAE model such that it becomes well-posed. For well-posed models, it is then discussed how particle filters can be implemented for estimating the time-varying variables in the model.

    The final topic in the thesis is model reduction of nonlinear DAE models. The objective with model reduction is to reduce the number of states, while not affecting the input-output behavior too much. Three different approaches are studied, namely balanced truncation, balanced truncation using minimization of the co-observability function and balanced residualization. To compute the reduced model for the different approaches, a method originally derived for nonlinear state-space models is extended to DAE models.

  • 17.
    Sjöberg, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Some Results On Optimal Control for Nonlinear Descriptor Systems2006Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [sv]

    I denna avhandling studeras optimal återkopplad styrning av olinjära deskriptorsystem. Ett deskriptorsystem är en matematisk beskrivning som kan innehålla både differentialekvationer och algebraiska ekvationer. En av anledningarna till intresset för denna klass av system är att objekt-orienterade modelleringsverktyg ger systembeskrivningar på denna form. Här kommer det att antas att det, åtminstone lokalt, är möjligt att eliminera de algebraiska ekvationerna och få ett system på tillståndsform. Teoretiskt är detta inte så inskränkande för genom att använda någon indexreduktionsmetod kan ganska generella deskriptor\-system skrivas om så att de uppfyller detta antagande.

    För system på tillståndsform kan Hamilton-Jacobi-Bellman-ekvationen användas för att bestämma den optimala återkopplingen. Ett liknande resultat finns för deskriptor\-system där istället en Hamilton-Jacobi-Bellman-liknande ekvation ska lösas. Denna ekvation innehåller dock en extra term för att hantera de algebraiska ekvationerna. Eftersom antagandena i denna avhandling gör det möjligt att skriva om deskriptorsystemet som ett tillståndssystem, undersöks hur denna extra term måste väljas för att båda ekvationerna ska få samma lösning.

    Ett problem med att beräkna den optimala återkopplingen med hjälp av Hamilton-Jacobi-Bellman-ekvationen är att det leder till att en olinjär partiell differentialekvation ska lösas. Generellt har denna ekvation ingen explicit lösning. Ett lättare problem är att beräkna en lokal optimal återkoppling. För analytiska system på tillståndsform löstes detta problem på 1960-talet och den optimala lösningen beskrivs av serieutvecklingar. I denna avhandling generaliseras detta resultat så att även deskriptor-system kan hanteras. Metoden illustreras med ett exempel som beskriver en faslåsande krets.

    I många situationer vill man veta om ett område är möjligt att nå genom att styra på något sätt. För linjära tidsinvarianta system fås denna information från styrbarhetgramianen. För olinjära system används istället styrbarhetsfunktionen. Tre olika metoder för att beräkna styrbarhetsfunktionen har härletts i denna avhandling. De framtagna metoderna är också applicerade på några exempel för att visa beräkningsstegen.

    Dessutom har observerbarhetsfunktionen studerats. Observerbarhetsfunktionen visar hur mycket utsignalenergi ett visst initial tillstånd svarar mot. Ett par olika metoder för att beräkna observerbarhetsfunktionen för deskriptorsystem tagits fram. För att beskriva en av metoderna, studeras ett litet exempel bestående av en elektrisk krets.

  • 18.
    Sjöberg, Johan
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Findeisen, Rolf
    Otto von Guericke University Magdeburg, Germany.
    Allgower, Frank
    University of Stuttgart, Germany.
    Model Predictive Control of Continuous Time Nonlinear Differential Algebraic Systems2007Inngår i: Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems, 2007, s. 48-53Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This work presents a sampled-data nonlinear model predictive control scheme with guaranteed stability for differential-algebraic systems. The main challenge is the avoidance of impulsive solutions due to discontinuities in the input or its derivatives. This is guaranteed by requiring the applied input to be sufficiently smooth. Stability is guaranteed by a terminal penalty term, together with a terminal region constraint. The control scheme is illustrated considering the control of an electrical circuit.

  • 19.
    Sjöberg, Johan
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Glad, Torkel
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Computing the Controllability Function for Nonlinear Descriptor Systems2006Inngår i: Proceedings of the 2006 American Control Conference, 2006, s. 1027-1031Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The computation of the controllability function for nonlinear descriptor systems is considered. Three different methods are derived. The first method is based on the necessary conditions for optimality from the Hamilton-Jacobi-Bellman theory for descriptor systems. The second method uses completion of squares to find the solution. The third method gives a series expansion solution, which with a finite number of terms can serve as an approximate solution.

  • 20.
    Sjöberg, Johan
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Glad, Torkel
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Computing the Controllability Function for Nonlinear Descriptor Systems2005Rapport (Annet vitenskapelig)
    Abstract [en]

    The computation of the controllability function for nonlinear descriptor systems is considered. Three different methods are derived. The first method is based on the necessary conditions for optimality from the Hamilton-Jacobi-Bellman theory for descriptor systems. The second method uses completion of squares to find the solution. The third method gives a series expansion solution, which with a finite number of terms can serve as an approximate solution.

  • 21.
    Sjöberg, Johan
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Glad, Torkel
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Power Series Solution of the Hamilton-Jacobi-Bellman Equation for DAE Models with a Discounted Cost2008Rapport (Annet vitenskapelig)
    Abstract [en]

    This paper considers infinite horizon optimal feedback control of nonlinear models with discounted cost. The paper includes two extensions of existing results about optimal feedback control. First, it is proven that for real analytic statespace models, a time-invariant real analytic feedback solution exists, even when the cost function includes a discount factor, provided certain regularity conditions. Second, the result is generalized to nonlinear DAE models. The feedback solution is valid in a neighborhood of the origin. In both cases, explicit formulas for the series expansions of the cost function and control law are given.

  • 22.
    Sjöberg, Johan
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Glad, Torkel
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Power Series Solution of the Hamilton-Jacobi-Bellman Equation for DAE Models with a Discounted Cost2008Inngår i: Proceedings of the 47th IEEE Conference on Decision and Control, 2008, s. 4761-4766Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper considers infinite horizon optimal feedback control of nonlinear models with discounted cost. The paper includes two extensions of existing results about optimal feedback control. First, it is proven that for real analytic statespace models, a time-invariant real analytic feedback solution exists, even when the cost function includes a discount factor, provided certain regularity conditions. Second, the result is generalized to nonlinear DAE models. The feedback solution is valid in a neighborhood of the origin. In both cases, explicit formulas for the series expansions of the cost function and control law are given.

  • 23.
    Sjöberg, Johan
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Glad, Torkel
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Descriptor Systems2005Inngår i: Proceedings of the 44th IEEE Conference on Decision and Control, 2005, s. 6869-6874Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Optimal control problems for a class of nonlinear descriptor systems are considered. It is shown that they possess a well-defined analytical feedback solution in a neighborhood of the origin, provided stabilizability and some other regularity conditions are satisfied. Explicit formulas for the series expansions of the cost function and control law are given.

  • 24.
    Sjöberg, Johan
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Glad, Torkel
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Descriptor Systems2005Rapport (Annet vitenskapelig)
    Abstract [en]

    Optimal control problems for a class of nonlinear descriptor systems are considered. It is shown that they possess a well-defined analytical feedback solution in a neighborhood of the origin, provided stabilizability and some other regularity conditions are satisfied. Explicit formulas for the series expansions of the cost function and control law are given.

  • 25.
    Sjöberg, Johan
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Glad, Torkel
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Time-Varying Differential-Algebraic Equations2006Inngår i: Proceedings of the 45th IEEE Conference on Decision and Control, 2006, s. 870-875Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Optimal control problems for a class of nonlinear time-varying differentialalgebraic equations are considered. It is shown that they possess a welldefined feedback solution in a neighborhood of the origin. Explicit formulasfor the series expansions of the cost function and control law are given.

  • 26.
    Sjöberg, Johan
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Glad, Torkel
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Time-Varying Differential-Algebraic Equations2006Inngår i: Proceedings of Reglermöte 2006, 2006Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Optimal control problems for a class of nonlinear time-varying differentialal gebraic equations are considered. It is shown that they possess a well defined feedback solution in a neighborhood of the origin. Explicit formulas for the series expansions of the cost function and control law are given.

  • 27.
    Sjöberg, Johan
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Glad, Torkel
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Time-Varying Differential-Algebraic Equations2007Rapport (Annet vitenskapelig)
    Abstract [en]

    Optimal control problems for a class of nonlinear time-varying differential-algebraic equations are considered. It is shown that they possess a well-defined feedback solution in a neighborhood of the origin. Explicit formulas for the series expansions of the cost function and control law are given.

  • 28.
    Sjöberg, Johan
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Glad, Torkel
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Rational Approximation of Nonlinear Optimal Control Problems2008Inngår i: Proceedings of the 17th IFAC World Congress, 2008, s. 11340-11345Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper rational approximation of solutions to nonlinear optimal control problems is considered. A computational procedure is presented that makes it possible to compute a rational function that approximates the true optimal cost function. It is shown that the rational function has the same series expansion around the origin as the true solution. Finally, two examples are given that compares the new method with the power series approximation, which is a rather well-known method to find approximative solutions.

  • 29.
    Sjöberg, Johan
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Glad, Torkel
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Fujimoto, Kenji
    Nagoya University, Japan.
    Model Reduction of Nonlinear Differential-Algebraic Equations2007Inngår i: Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems, 2007, s. 176-181Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this work, a computational method to compute balanced realizations for nonlinear differential-algebraic equation systems is derived. The work is a generalization of an earlier work for nonlinear control-affine systems, and is based on analysis of the controllability and observability functions.

  • 30.
    Sjöberg, Johan
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Lindkvist, Simon
    ABB, Sweden.
    Linder, Jonas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Daneryd, Anders
    ABB, Sweden.
    Interactive Multiobjective Optimization for the Hot Rolling Process2012Inngår i: Proceedings of 51st IEEE Conference on Decision and Control, 2012, s. 7030-7036Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper, multi-objective optimization is applied to the hot rolling process. It is modeled mostly using first principle models considering, for instance, the mass balance (or mass flow rate), the tensions in the material, the power requirements, the thermal field, and the microstructure of the material.

    Two optimization formulations are considered. In the first case, both the grain size and the power consumption in the rolling process are minimized. It is shown that the result from a single-objective optimization formulation, i.e., where only one of the two objectives are considered, yields control schedules with poor performance for the other objective. Furthermore, the differences between optimal control schedules for different objectives are compared and analyzed. The second case is a design optimization problem where the optimal positioning of cooling pipes is considered. This study shows how the MOO framework can be used to systematically choose a good cooling pipe setup. 

    The two studies shows that MOO can be a helpful tool when designing and running hot rolling processes. Furthermore, navigation among the Pareto optimal solutions is very useful when the user wants to learn how the control variables interact with the process.

1 - 30 of 30
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